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A right-wing Israeli government, led by Prime Minister Benjamin Netanyahu, was sworn in on Tuesday, and its refusal to accept a two-state solution with the Palestinians has already set it on a collision course with the Obama Administration.

Netanyahu's showdown with Washington may happen soon. Leader of the hawkish Likud Party, Netanyahu will meet with U.S. Middle East envoy George Mitchell in Jerusalem on April 16. That meeting will be a dress rehearsal for the Prime Minister's trip to Washington in May for talks with President Barack Obama and Secretary of State Hillary Clinton, who are pushing for the creation of a Palestinian state in the West Bank and Gaza as a key to a wider peace in the region. (See pictures of heartbreak in the Middle East.)

In his swearing-in speech before the Knesset, Netanyahu appeared to soften his tough stance on the Palestinians, directing his words as much toward Washington as to Ramallah, the seat of the Palestinian Authority. Netanyahu, who leads a sprawling coalition of right-wing and religious parties that is tempered by the center-left Labor Party, vowed to improve economic, security and political ties with Israel's Arab neighbors. "We do not want to rule the Palestinians," he said. But nowhere in his speech did he mention the two-state solution championed by Washington. (See pictures of 60 years of Israel.)

Palestinians reacted to Netanyahu's swearing-in with deep pessimism. Senior advisers to Palestinian Authority President Mahmoud Abbas told TIME that after having failed to extract any concessions from former Israeli Premier Ehud Olmert, Abbas expects even less progress from Netanyahu on such key issues as a halt to the construction of illegal Jewish settlements and the removal of more than 550 army checkpoints in the West Bank, which are paralyzing the movement of Palestinians. These sources told TIME that Abbas  who not only confronts a new, hawkish Israeli government but also the loss of the Gaza Strip to Islamic militants Hamas  confided to aides that he may resign over his frustrations with Israel. "The only hope which keeps Abbas breathing politically is that Obama may seriously pressure Israel to start negotiating for a two-state solution," a senior aide said.

In Gaza, a Hamas official told TIME that Netanyahu's victory was "proof that Israelis are opposed to giving the Palestinians anything." He added, "Netanyahu only believes in escalating the military solution against us."

But in Washington, at least, the vague outlines of an Obama-sponsored peace plan are starting to take shape. The Israeli press say that U.S. envoy Mitchell will propose a new formula to Netanyahu: an Israeli withdrawal to the 1967 borders, excepting the large Jewish settlements around Jerusalem; having Jerusalem as the capital of both Israel and a future Palestine; the adoption of a special status for the Old City, holy to Christians, Jews and Muslims; the return of refugees to a Palestinian state, with Israel accepting some responsibility for their plight; and the presence of a multinational force in the Palestinian territories during an interim period to guarantee Israel's security from terrorist attacks. (See pictures of Israeli soldiers sweeping into Gaza.)

Netanyahu may viscerally oppose this plan. Even if he does not, selling it to his right-wing coalition partners may prove impossible. They refuse to divide Jerusalem and want to plow ahead with more Jewish settlements in the West Bank. As part of a coalition dealmaker, Netanyahu pledged to allow the construction of a new settlement of 3,500 dwellings outside Jerusalem that would surround the city's Arab neighborhoods. And his choice for Foreign Minister, Avigdor Lieberman, who has pronounced anti-Arab views and is under criminal investigation for allegedly taking bribes, has left the Americans and the Europeans less than enthused. (See a TIME video on Lieberman.)

For weeks, Netanyahu struggled to build a coalition. The result is a Rube Goldberglike contraption with 30 Cabinet ministers and seven deputy ministers. (Britain, a nation nearly 10 times the size of Israel, has only 22 Cabinet ministers.) Opposition leader Tzipi Livni, of the centrist Kadima Party, called the new government "bloated" with "ministers of nothing." A Haaretz poll shows that, with Netanyahu's leadership less than 24 hours old, 54% of Israelis are "unhappy" with his sprawling government, leading one Israeli pundit to comment (using the politician's nickname), "Bibi's period of grace lasted for all of 10 seconds."

Netanyahu does, however, have a few strong cards. His coalition passed the Knesset vote with 69 out of 120 seats, a huge margin by Israel's fractious standards. He has shown himself to be a shrewd deal spinner, and his government may stand a better chance of arm-twisting the Knesset into accepting a U.S.-sponsored peace deal than a weak, center-left government ever could. As for Lieberman's belligerent views toward Arabs, Netanyahu aides hasten to say the Premier himself will handle ties with Washington and Arab neighbors. (See pictures of life under Hamas in Gaza.)

The sad fact is that most Israelis care less about peace with the Palestinians than they do about the failing economy and the perceived nuclear threat from Iran, and the election results show that they see "Bibi" as stronger on both counts.

Still, Netanyahu ignores the Palestinians at his peril; Hamas is rearming itself in Gaza for a new round of fighting, and there are rumblings of another intifadeh, or uprising, breaking out in the West Bank. And a wider peace with Arab nations will depend on Israel's letting the Palestinians have a state. In his farewell speech, outgoing Premier Olmert warned, "There is no state of Israel without a solid Jewish majority, and there is no Jewish majority in Greater Israel [including the West Bank], which is home to millions of Palestinians." Olmert lacked the courage and the political backing to help the Palestinians create a state. Now it's Netanyahu's turn.
 With reporting by Jamil Hamad / Ramallah